10 logging firms use a forest to collect timber. Each firm must choose how many trees to cut, 9;. The benefit of cutting a tree is 1000-2G per tree, where G is the total quantity of trees cut in the forest. The marginal cost of cutting a tree is 10G. Firms do not face any fixed costs. The social optimum solves: max(1000-2G)G-10G O O max (1000-2G)G-5G² O max 9, (1000-2G)g₁ - 10g; 9₁ O max (1000-2G)g, -5g?
10 logging firms use a forest to collect timber. Each firm must choose how many trees to cut, 9;. The benefit of cutting a tree is 1000-2G per tree, where G is the total quantity of trees cut in the forest. The marginal cost of cutting a tree is 10G. Firms do not face any fixed costs. The social optimum solves: max(1000-2G)G-10G O O max (1000-2G)G-5G² O max 9, (1000-2G)g₁ - 10g; 9₁ O max (1000-2G)g, -5g?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![10 logging firms use a forest to collect timber. Each firm must choose how many trees to
cut, 9₁. The benefit of cutting a tree is 1000-2G per tree, where G is the total
quantity of trees cut in the forest. The marginal cost of cutting a tree is 100. Firms do not
face any fixed costs. The social optimum solves:
O max (1000-2G)G-10G
O max(1000-2G)G-5G²
O max, (1000-2G)g₁ - 10g;
O max, (1000-2G)g;- 5g7](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3e37d0a9-74c8-4250-9a21-add329f5d305%2F535b991b-1ccf-4af3-9dcb-d9ed5ce3d731%2Fl5ncb_processed.png&w=3840&q=75)
Transcribed Image Text:10 logging firms use a forest to collect timber. Each firm must choose how many trees to
cut, 9₁. The benefit of cutting a tree is 1000-2G per tree, where G is the total
quantity of trees cut in the forest. The marginal cost of cutting a tree is 100. Firms do not
face any fixed costs. The social optimum solves:
O max (1000-2G)G-10G
O max(1000-2G)G-5G²
O max, (1000-2G)g₁ - 10g;
O max, (1000-2G)g;- 5g7
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